Basic Limit Laws. 2.3. Theorem 1: Basic Limit Laws. If lim x →c f(x) and lim x→c g(x) exist, then Sum Law: lim x→c (f(x) + g(x)) exists and lim x→c (f(x) + g(x)) = lim x→c f(x) + lim x→c g(x).
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If lim x→c f(x) and lim x→c g(x) exist, then
lim x→c g(x).
Substitution can be used to evaluate limits when the function is continuous.